An imaging or rendering device, such as a printer or copier, typically creates images using combinations of four colors of marking agents or colorants, such as cyan, magenta, yellow and black (CMYK). The images are created based on image data which assigns at least one of the four colors and a numerical color intensity or input color value to each picture element or pixel in the image.
A variety of factors contribute to unintentional color variations. One problem is that, due to manufacturing variations, different imaging devices can output different intensities of color based on identical image data. For example, the density of the toner laid down on the print medium determines the color intensity. The denser or thicker the toner is laid down on a white print medium such as paper, the less white is visible through the toner on the paper. Consequently, the denser the toner, the less the lightness of the toner color, and the greater the intensity of the toner color.
Because there is such variation in color laid down by different imaging devices based on identical image data, color intensities that are output by some imaging devices can be outside of an acceptable range. Thus, in order to ensure that each imaging device outputs color intensities that closely correspond to the color intensities specified by the image data, each imaging device is typically calibrated to output appropriate color intensities.
For purposes such as printer color calibration, it is typically necessary to estimate the average response of the printer to different input colors. Such measurements are complicated by the fact that the response is typically confounded with spatial non-uniformity, such as banding. In order to assess the average response, measurements are taken over large segments in the process direction, with the hope of “averaging out” most of the variation caused by banding. This is very costly, especially for on-line color calibration systems, which need to operate with a minimum number of test patterns. Alternatively, patches of a given color have been replicated at random locations throughout the page. This simultaneously reduces the effects of streaks and bands, but is sub-optimal for bands.
FIG. 1 illustrates what a typical profile might look like in the presence of banding. The profile shows a response R measured as a function of the position, x, in the process direction. The measured response R could take a variety of forms including, for example, L* measured on paper. However, this discussion also applies in general, for example, to any applications where the appropriate measurements are performed, such as within the marking engine before transfer to paper, e.g. measurements on a photoreceptor belt.
In practice, each data point R(x) would be obtained by sensing R over a finite distance DX in the process direction and a finite distance DY in the cross-process direction. The size of the sample area given by DX and DY would be required to exceed a certain minimum, in order to address noise in both the printing process and sensing.
As seen from the illustration, any measurement where DX is small compared to the spatial scale of the variation will likely lead to erroneous estimates of the average response <R>. To minimize the error, the standard approach is to increase DX to the point where it is large enough that the variation is “averaged out.” In practice, significant variations might be caused by problems such as once-around signatures, which can have a very long period, requiring DX, in some cases, to be in excess of 10 inches. In comparison, the mentioned minimum size of DX due to noise might be significantly less than one inch.
Alternatively, a statistical average can be calculated by replicating patches of a given color at pseudo-random locations throughout a larger region. This approach simultaneously reduces the effects of both banding and other non-uniformities, but is sub-optimal for banding. The situation is further complicated when multiple incommensurable banding frequencies are involved, in which case very large DX would be required to estimate the average <R>.